Relevant bibliographies by topics / Z-polytopes

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Z-polytopes'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Z-polytopes"

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Clingher, Adrian, and Jae-Hyouk Lee. "Lorentzian Lattices and E-Polytopes." Symmetry 10, no. 10 (2018): 443. http://dx.doi.org/10.3390/sym10100443.

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We consider certain E n -type root lattices embedded within the standard Lorentzian lattice Z n + 1 ( 3 ≤ n ≤ 8 ) and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice Z n + 1 decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type ( n − 4 ) 21 .
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Ryshkov, S. S., and R. M. Erdahl. "The Empty Sphere Part II." Canadian Journal of Mathematics 40, no. 5 (1988): 1058–73. http://dx.doi.org/10.4153/cjm-1988-043-5.

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Blow up a sphere in one of the interstices of a lattice until it is held rigidly. There will be no lattice points in the interior and sufficiently many on the boundary so that their convex hull is a solid figure. Such a sphere was called an empty sphere by B. N. Delone in 1924 when he introduced his method for lattice coverings [3, 4]. The circumscribed polytope is called an L-polytope. Our interest in such matters stems from the following result [6, Theorems 2.1 and 2.3]: With a list of the L-polytopes for lattices of dimension ≦n one can give a geometrical description of the possible sets of
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Beben, Piotr, and Jelena Grbić. "LS-category of moment-angle manifolds and higher order Massey products." Forum Mathematicum 33, no. 5 (2021): 1179–205. http://dx.doi.org/10.1515/forum-2021-0015.

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Abstract Using the combinatorics of the underlying simplicial complex K, we give various upper and lower bounds for the Lusternik–Schnirelmann (LS) category of moment-angle complexes 𝒵 K {\mathcal{Z}_{K}} . We describe families of simplicial complexes and combinatorial operations which allow for a systematic description of the LS-category. In particular, we characterize the LS-category of moment-angle complexes 𝒵 K {\mathcal{Z}_{K}} over triangulated d-manifolds K for d ≤ 2 {d\leq 2} , as well as higher-dimensional spheres built up via connected sum, join, and vertex doubling operations. We sh
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Hartley, Michael I. "Covers ℘ for Abstract Regular Polytopes $\mathcal {Q}$ such that $\mathcal{Q}=\mathcal{P}/\mathbf{Z}_{p}^{k}$." Discrete & Computational Geometry 44, no. 4 (2009): 844–59. http://dx.doi.org/10.1007/s00454-009-9234-7.

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Kabluchko, Zakhar, and Dmitry Zaporozhets. "Absorption probabilities for Gaussian polytopes and regular spherical simplices." Advances in Applied Probability 52, no. 2 (2020): 588–616. http://dx.doi.org/10.1017/apr.2020.7.

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AbstractThe Gaussian polytope $\mathcal P_{n,d}$ is the convex hull of n independent standard normally distributed points in $\mathbb{R}^d$ . We derive explicit expressions for the probability that $\mathcal P_{n,d}$ contains a fixed point $x\in\mathbb{R}^d$ as a function of the Euclidean norm of x, and the probability that $\mathcal P_{n,d}$ contains the point $\sigma X$ , where $\sigma\geq 0$ is constant and X is a standard normal vector independent of $\mathcal P_{n,d}$ . As a by-product, we also compute the expected number of k-faces and the expected volume of $\mathcal P_{n,d}$ , thus rec
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Cunningham, Gabe. "Mixing chiral polytopes." Journal of Algebraic Combinatorics 36, no. 2 (2011): 263–77. http://dx.doi.org/10.1007/s10801-011-0335-z.

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Stenson, Catherine. "Families of Tight Inequalities for Polytopes." Discrete & Computational Geometry 34, no. 3 (2005): 507–21. http://dx.doi.org/10.1007/s00454-005-1193-z.

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Bisztriczky, Tibor, K�roly B�r�czky, Jr., and David S. Gunderson. "Cyclic polytopes, hyperplanes, and Gray codes." Journal of Geometry 78, no. 1-2 (2003): 25–49. http://dx.doi.org/10.1007/s00022-003-1705-z.

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9

Barvinok, Alexander, Seung Jin Lee, and Isabella Novik. "Centrally symmetric polytopes with many faces." Israel Journal of Mathematics 195, no. 1 (2012): 457–72. http://dx.doi.org/10.1007/s11856-012-0107-z.

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Fredrickson, Karl. "Extremal Transitions from Nested Reflexive Polytopes." Communications in Mathematical Physics 335, no. 3 (2014): 1381–95. http://dx.doi.org/10.1007/s00220-014-2201-z.

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Dissertations / Theses on the topic "Z-polytopes"

1

Seghir, Rachid. "Méthodes de dénombrement de points entiers de polyèdres et applications à l'optimisation de programmes." Université Louis Pasteur (Strasbourg) (1971-2008), 2006. https://publication-theses.unistra.fr/public/theses_doctorat/2006/SEGHIR_Rachid_2006.pdf.

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Le modèle polyédrique est un formalisme utilisé en optimisation automatique de programmes. Il permet notamment de représenter les itérations et les références à des tableaux, dans des nids de boucles affines, par des points à coordonnées entières de polyèdres bornés, ou Z-polytopes (paramétrés). Dans cette thèse, trois nouveaux algorithmes de dénombrement ont été développés : des points entiers dans un Z-polytope paramétré, dans une union non disjointe de Z-polytopes paramétrés et dans leurs images par des fonctions affines. Le résultat de ces dénombrements est donné par un ou plusieurs polynô
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Book chapters on the topic "Z-polytopes"

1

Schwartz, Richard Evan. "The Orbit Equivalence Theorem." In The Plaid Model. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691181387.003.0018.

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This chapter begins Part 4 of the monograph. The goal of this part is to prove the Orbit Equivalence Theorem and the Quasi-Isomorphism Theorem. Theorem 17.1 (Orbit Equivalence) states that there is a dynamically large subset Z ⊂ X and a map Ω‎: Z → Y. Section 17.2 defines Z. Section 17.3 defines Ω‎. Section 17.4 characterizes the image Ω‎(Z). Section 17.5 defines a partition of Z into small convex polytopes which have the property that all the maps in Equations 17.1 and 1 are entirely defined and projective on each polytope. This allows us to verify the properties in the Orbit Equivalence Theorem just by checking what the two relevant maps do to the vertices of the new partition. Section 17.6 puts everything together and prove the Orbit Equivalence Theorem modulo some integer computer calculations. Section 17.7 discusses the computational techniques used to carry out the calculations from Section 17.6. Section 17.8 explains the calculations.
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Journal articles
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